On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials

Zhuk, Ya. A.; Сенченков, И. К.

doi:10.1007/s10778-006-0076-1

Cited by 6 publications

(2 citation statements)

References 9 publications

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“…The piezoelectric effect is manifested as electrically induced forcesÑ E and momentsM E in the relations (18).…”

Section: Formulation Of the Coupled Electromechanical Problem For An mentioning

confidence: 99%

“…response [17]. Under some circumstances, the geometrical nonlinearity has to be taken into account as well [12,18]. With these added complications, the correct prediction and simulation of complex dynamic and quasi-static processes in thin-wall inelastic passive and active members taking account of electromechanical coupling is still a challenge.…”

Section: Introductionmentioning

confidence: 99%

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Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

2010

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A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff-Love hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam, whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied. Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified model. Limitations on the simplified model application are specified.

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“…The piezoelectric effect is manifested as electrically induced forcesÑ E and momentsM E in the relations (18).…”

Section: Formulation Of the Coupled Electromechanical Problem For An mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

2010

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Fundamentals of viscoelastoplasticity and hardening theory revisited

Khoroshun

2008

Int Appl Mech

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Thermodynamic and statistical methods for setting up the constitutive equations describing the viscoelastoplastic deformation and hardening of materials are proposed. The thermodynamic method is based on the law of conservation of energy, the equations of entropy balance and entropy production in the presence of self-balanced internal microstresses characterized by conjugate hardening parameters. The general constitutive equations include the relationships between the thermodynamic flows and forces, which follow from nonnegative entropy production and satisfy the generalized Onsager's principle, and the thermoelastic relations and the expression for entropy, which follow from the law of conservation of energy. Specific constitutive equations are derived by representing the dissipation rate as a sum of two terms responsible for kinematic and isotropic hardening and approximated by power and hyperbolic-sinus functions. The constitutive equations describing viscoelastoplastic deformation and hardening are derived based on stochastic microstructural concepts and on the linear thermoelasticity model and nonlinear Maxwell model for the spherical and deviatoric components of microstresses and microstrains, respectively. The problem of determining the effective properties and stress-strain state of a three-component material found using the Voigt-Reuss scheme leads to constitutive equations similar in form to those produced by the thermodynamic method Introduction. For theoretical descriptions of the viscoelastoplastic behavior of structural members under mechanical and thermal loads to be reliable, it is first necessary to set up appropriate constitutive equations or to establish relationships between the dynamic and kinematic parameters, taking into account the physical phenomena accompanying viscoelastoplastic deformation. Such phenomena include conversion of work into heat and strain energy, hardening, Bauschinger effect, aftereffect, relaxation, and dependence of hardening on inelastic strain rate. One of the most significant criteria that a complex model is adequate and correct is its consistency with the simpler models generalized by it. In our case, this means that the constitutive equations describing elastic deformation, viscous flow, and plastic deformation should follow, as partial or limiting cases, from the constitutive equations of viscoelastoplasticity.Recently, the theory and problems of viscoelastoplasticity have widely used the Bodner-Partom model [7,8,[12][13][14][15][20][21][22][23], which, along with stresses and strains, uses internal variables describing isotropic and kinematic hardening for which evolutionary equations are formulated. In this model, strains have elastic and inelastic components, and inelastic strain rates are specified as a negative exponential function of the ratio of the sum of hardening parameters to stresses. A serious shortcoming of this model is inconsistency-in the specific case of zero hardening parameters, the law of viscous flow does not follow from the constitutive equ...

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Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

Chervinko

Сенченков

2008

Int Appl Mech

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The Bodner-Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strainand stress-controlled cycles of loading in the temperature range 20-400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence Introduction. Modeling the mechanical behavior of inelastic materials and structural members under cyclic loading is of theoretical and practical importance in studying the dissipation and accumulation of energy in materials, evaluating the highand low-cycle fatigue of structural members, damping vibrations, etc. [9,10,15,18,[20][21][22].A fundamental result in the theory of linear viscoelasticity is experimental and theoretical justification of the concept of complex mechanical characteristics that describe the behavior of a material under harmonic loading [1,3,11,17]. In these publications, the concept of complex characteristics was generalized to nonisothermal processes for specific classes (thermorheologically simple) materials. In linear viscoelasticity, the complex characteristics provide an exact description of the mechanical behavior of materials in stationary processes. For physically nonlinear materials, this concept was used together with various schemes of harmonic linearization to develop approximate models. The capabilities of these schemes were studied in [5,7,8]. It was established in [12,13] that determining the complex characteristics is an ambiguous procedure, and its result is greatly dependent on the choice of a functional space whose norm is used to approximate nonlinear (generally, polyharmonic) reactions of a material to harmonic loading by a monoharmonic process. By using a mechanical interpretation for such a norm, it is possible to find an approximation corresponding to the mechanical problem of interest. Relevant results are reviewed in [4,19].The publications cited above deal with isothermal processes. The complex characteristics are assumed independent of temperature. Such a model is applicable when thermal perturbations are small. It is obvious that it cannot describe such important processes as vibrational heating under loading of high amplitudes and vibrations at high external temperatures. Moreover, in justifying the concept of complex characteristics for nonlinear materials, it is of practical and methodological importance to test the principle of correspondence between the modulus and the compliance in the cases of soft (stress-controlled) and hard (strain-controlled) cyclic loading.The present paper uses the complete system of equations of the nonisothermal Bodner-...

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On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials

Cited by 6 publications

References 9 publications

Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

Simplified monoharmonic approach to investigation of forced vibrations of thin wall multilayer inelastic elements with piezoactive layers under cyclic loading

Fundamentals of viscoelastoplasticity and hardening theory revisited

Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

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